Einstein-Podolsky-Rosen (EPR) entanglement introduced in 1935 deals with two particles that are entangled in their positions and momenta. Here we report the first experimental demonstration of EPR position-momentum entanglement of narrowband photon pairs generated from cold atoms. By using two-photon quantum ghost imaging and ghost interference, we demonstrate explicitly that the narrowband photon pairs violate the separability criterion, confirming EPR entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons. Our new source of EPR-entangled narrowband photons is expected to play an essential role in spatially-multiplexed quantum information processing, such as, storage of quantum correlated images, quantum interface involving hyper-entangled photons, etc.Entanglement, initially explored experimentally with the polarization states of a pair of photons [1, 2], has now been demonstrated in a variety of physical systems, e.g., two spontaneous parametric down-conversion (SPDC) photons [3, 4], two-mode squeezed states of optical fields [5, 6], trapped ions [7, 8], neutral atoms [9, 10], and artificial quantum systems [11, 12]. The gedankenexperiment proposed by Einstein-Podolsky-Rosen (EPR) in 1935, on the other hand, involves a pair of particles that are entangled in their positions and momenta [13][14][15]. In addition to fundamental interests, EPR entanglement is essential in quantum imaging and quantum metrology [16][17][18][19]. Here we report EPR position-momentum entanglement of narrowband (∼ MHz) photon pairs generated from χ (3) spontaneous four-wave mixing (SFWM) in a cold atomic ensemble. By using two-photon quantum ghost imaging and interference [20,21], we demonstrate explicitly that the narrowband photon pairs violate the separability criterion, confirming EPR positionmomentum entanglement. We further demonstrate continuous variable EPR steering for positions and momenta of the two photons [22][23][24][25][26][27][28]. To the best of our knowledge, this is the first experimental demonstration of EPR entanglement and EPR steering of position-momentum degrees of freedom of narrowband photon pairs, well suited for spatially-multiplexed quantum information processing, storage of quantum images, quantum interface involving hyper-entangled photons, etc [29][30][31][32][33][34].The position-momentum-like continuous variable feature of EPR entanglement has been explored initially by using quadrature-phase amplitudes of two-mode squeezed states [5, 6]. Genuine EPR position-momentum entanglement of photon pairs became available later by the SPDC process in a bulk crystal [14,15] and is thought to be essential in quantum imaging and quantum metrology [16][17][18][19]. The EPR-entangled SPDC photons, however, are inherently broadband, typically on the order of several THz in bandwidth. This large bandwidth makes the source unsuitable for interfacing with quantum memory based on atom-photon coherent interaction, which typically has the working bandwidth of a ...